ALBERT

Description: A database of transitional direct numerical simulation (DNS) realizations of a supercritical mixing layer is analysed for understanding small-scale behaviour and examining subgrid-scale (SGS) models duplicating that behaviour. Initially, the mixing layer contains a single chemical species in each of the two streams, and a perturbation promotes roll-up and a double pairing of the four spanwise vortices initially present. The database encompasses three combinations of chemical species, several perturbation wavelengths and amplitudes, and several initial Reynolds numbers specifically chosen for the sole purpose of achieving transition. The DNS equations are the Navier-Stokes, total energy and species equations coupled to a real-gas equation of state; the fluxes of species and heat include the Soret and Dufour effects. The large-eddy simulation (LES) equations are derived from the DNS ones through filtering. Compared to the DNS equations, two types of additional terms are identified in the LES equations: SGS fluxes and other terms for which either assumptions or models are necessary. The magnitude of all terms in the LES conservation equations is analysed on the DNS database, with special attention to terms that could possibly be neglected. It is shown that in contrast to atmospheric-pressure gaseous flows, there are two new terms that must be modelled: one in each of the momentum and the energy equations. These new terms can be thought to result from the filtering of the nonlinear equation of state, and are associated with regions of high density-gradient magnitude both found in DNS and observed experimentally in fully turbulent high-pressure flows. A model is derived for the momentum-equation additional term that performs well at small filter size but deteriorates as the filter size increases, highlighting the necessity of ensuring appropriate grid resolution in LES. Modelling approaches for the energy-equation additional term are proposed, all of which may be too computationally intensive in LES. Several SGS flux models are tested on an a priori basis. The Smagorinsky (SM) model has a poor correlation with the data, while the gradient (GR) and scale-similarity (SS) models have high correlations. Calibrated model coefficients for the GR and SS models yield good agreement with the SGS fluxes, although statistically, the coefficients are not valid over all realizations. The GR model is also tested for the variances entering the calculation of the new terms in the momentum and energy equations; high correlations are obtained, although the calibrated coefficients are not statistically significant over the entire database at fixed filter size. As a manifestation of the small-scale supercritical mixing peculiarities, both scalar-dissipation visualizations and the scalar-dissipation probability density functions (PDF) are examined. The PDF is shown to exhibit minor peaks, with particular significance for those at larger scalar dissipation values than the mean, thus significantly departing from the Gaussian behaviour. © 2007 Cambridge University Press.

Description: A model of multicomponent-liquid (MC-liquid) drop evaporation in a three-dimensional mixing layer is here exercised at larger Reynolds numbers than in a previous study, and transitional states are obtained. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete coupling between phases is included with source terms in the gas conservation equations accounting for the drop/flow interaction in terms of drop drag, drop heating and species evaporation. The liquid composition, initially specified as a single-Gamma (SG) probability distribution function (PDF) depending on the molar mass is allowed to evolve into a linear combination of two SGPDFs, called the double-Gamma PDF (DGPDF). The compositions of liquid and vapor emanating from the drops are calculated through four moments of the DGPDFs, which are drop-specific and location-specific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions and the effect of the initial mass loading and initial free-stream gas temperature are explored. For reference, Simulations are also performed for gaseous multicomponent mixing layers for which the effect of Reynolds number is investigated. The results encompass examination of the global layer characteristics, flow visualizations and homogeneous-plane statistics at transition. Comparisons are performed with previous pre-transitional MC-liquid simulations and with transitional single-component (SC) liquid studies. It is found that MCC flows at transition, the classical energy cascade is of similar strength, but that the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation in the former case. Contrasting to pre-transitional MC flows, the vorticity and drop organization depend on the initial gas temperature, this being due to the drop/turbulence coupling. The vapor-composition mean molar mass and standard deviation distributions strongly correlate with the initial liquid-composition PDF; such a correlation only exists for the magnitude of the mean but not for that of the standard deviation. Unlike in pre-transitional situations, regions of large composition standard deviation no longer necessarily coincide with regions of large mean molar mass. The kinetic energy, rotational and composition characteristics, and dissipation are liquid specific and the variation among liquids is amplified with increasing free-stream gas temperature. Eulerian and Lagrangian statistics of gas-phase quantities show that the different. Observation framework may affect the perception of the flow characteristics. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from a SGPDF. The PDF of the scalar dissipation rate is calculated for drop-laden layers and is shown to depart more significantly from the typically assumed Gaussian in gaseous flows than experimentally measured gaseous scalar dissipation rates, this being attributed to the increased heterogeneity due to drop/flow interactions.